Witt was the ace of the California Angels pitching staff from 1984 to 1988, before slipping noticeably to a 9-15, 4.59 record in 1989. Still, the New York Yankees acquired him early in the 1990 season in a trade for Dave Winfield, but Witt was done, winning only 8 more games between the trade and his last Major League appearance in 1993.

Witt was the starting pitcher for the Angels in the famous Game 5 of the 1986 ALCS on October 12, 1986. Having won Game 1 handily, he was cruising along with a 5-2 lead coming into the 9th inning, with the Angels holding a 3 game to 1 advantage over the Boston Red Sox. He gave up a two-run home run to Don Baylor and was lifted from the game by manager Gene Mauch after he retired the next batter, Dwight Evans, on a pop-up for the second out. However, relievers Gary Lucas and Donnie Moore were unable to hold the lead - with Dave Henderson's two-strike, two-run home run off Moore being the key blow - and the Red Sox won the game in 11 innings and the next two as well to advance to the 1986 World Series.